mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-10-31 13:10:19 -04:00
269 lines
9.7 KiB
C++
269 lines
9.7 KiB
C++
// Copyright John Maddock 2006.
|
|
// Copyright Paul A. Bristow 2007, 2010.
|
|
|
|
// Use, modification and distribution are subject to the
|
|
// Boost Software License, Version 1.0.
|
|
// (See accompanying file LICENSE_1_0.txt
|
|
// or copy at http://www.boost.org/LICENSE_1_0.txt)
|
|
|
|
// test_gamma_dist.cpp
|
|
|
|
// http://en.wikipedia.org/wiki/Gamma_distribution
|
|
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
|
|
// Also:
|
|
// Weisstein, Eric W. "Gamma Distribution."
|
|
// From MathWorld--A Wolfram Web Resource.
|
|
// http://mathworld.wolfram.com/GammaDistribution.html
|
|
|
|
#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
|
|
|
|
#include <boost/math/concepts/real_concept.hpp> // for real_concept
|
|
#define BOOST_TEST_MAIN
|
|
#include <boost/test/unit_test.hpp> // Boost.Test
|
|
#include <boost/test/floating_point_comparison.hpp>
|
|
|
|
#include <boost/math/distributions/gamma.hpp>
|
|
using boost::math::gamma_distribution;
|
|
#include <boost/math/tools/test.hpp>
|
|
#include "test_out_of_range.hpp"
|
|
|
|
#include <iostream>
|
|
#include <iomanip>
|
|
using std::cout;
|
|
using std::endl;
|
|
using std::setprecision;
|
|
#include <limits>
|
|
using std::numeric_limits;
|
|
|
|
template <class RealType>
|
|
RealType NaivePDF(RealType shape, RealType scale, RealType x)
|
|
{
|
|
// Deliberately naive PDF calculator again which
|
|
// we'll compare our pdf function. However some
|
|
// published values to compare against would be better....
|
|
using namespace std;
|
|
RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape;
|
|
return exp(result);
|
|
}
|
|
|
|
template <class RealType>
|
|
void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
|
|
{
|
|
BOOST_CHECK_CLOSE(
|
|
::boost::math::cdf(
|
|
gamma_distribution<RealType>(shape, scale), // distribution.
|
|
x), // random variable.
|
|
p, // probability.
|
|
tol); // %tolerance.
|
|
BOOST_CHECK_CLOSE(
|
|
::boost::math::cdf(
|
|
complement(
|
|
gamma_distribution<RealType>(shape, scale), // distribution.
|
|
x)), // random variable.
|
|
q, // probability complement.
|
|
tol); // %tolerance.
|
|
if(p < 0.999)
|
|
{
|
|
BOOST_CHECK_CLOSE(
|
|
::boost::math::quantile(
|
|
gamma_distribution<RealType>(shape, scale), // distribution.
|
|
p), // probability.
|
|
x, // random variable.
|
|
tol); // %tolerance.
|
|
}
|
|
if(q < 0.999)
|
|
{
|
|
BOOST_CHECK_CLOSE(
|
|
::boost::math::quantile(
|
|
complement(
|
|
gamma_distribution<RealType>(shape, scale), // distribution.
|
|
q)), // probability complement.
|
|
x, // random variable.
|
|
tol); // %tolerance.
|
|
}
|
|
// PDF:
|
|
BOOST_CHECK_CLOSE(
|
|
boost::math::pdf(
|
|
gamma_distribution<RealType>(shape, scale), // distribution.
|
|
x), // random variable.
|
|
NaivePDF(shape, scale, x), // PDF
|
|
tol); // %tolerance.
|
|
}
|
|
|
|
template <class RealType>
|
|
void test_spots(RealType)
|
|
{
|
|
// Basic sanity checks
|
|
//
|
|
// 15 decimal places expressed as a persentage.
|
|
// The first tests use values generated by MathCAD,
|
|
// and should be accurate to around double precision.
|
|
//
|
|
RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100;
|
|
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
|
|
|
|
check_gamma(
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(1),
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(0.682689492137085),
|
|
static_cast<RealType>(1-0.682689492137085),
|
|
tolerance);
|
|
check_gamma(
|
|
static_cast<RealType>(2),
|
|
static_cast<RealType>(1),
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(0.090204010431050),
|
|
static_cast<RealType>(1-0.090204010431050),
|
|
tolerance);
|
|
check_gamma(
|
|
static_cast<RealType>(40),
|
|
static_cast<RealType>(1),
|
|
static_cast<RealType>(10),
|
|
static_cast<RealType>(7.34163631456064E-13),
|
|
static_cast<RealType>(1-7.34163631456064E-13),
|
|
tolerance);
|
|
|
|
//
|
|
// Some more test data generated by the online
|
|
// calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
|
|
// This has the advantage of supporting the scale parameter as well
|
|
// as shape, but has only a few digits accuracy, and produces
|
|
// some deeply suspect values if the shape parameter is < 1
|
|
// (it doesn't agree with MathCAD or this implementation).
|
|
// To be fair the incomplete gamma is tricky to get right in this area...
|
|
//
|
|
tolerance = 1e-5f * 100; // 5 decimal places as a persentage
|
|
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
|
|
|
|
check_gamma(
|
|
static_cast<RealType>(2),
|
|
static_cast<RealType>(1)/5,
|
|
static_cast<RealType>(0.1),
|
|
static_cast<RealType>(0.090204),
|
|
static_cast<RealType>(1-0.090204),
|
|
tolerance);
|
|
check_gamma(
|
|
static_cast<RealType>(2),
|
|
static_cast<RealType>(1)/5,
|
|
static_cast<RealType>(0.5),
|
|
static_cast<RealType>(1-0.287298),
|
|
static_cast<RealType>(0.287298),
|
|
tolerance);
|
|
check_gamma(
|
|
static_cast<RealType>(3),
|
|
static_cast<RealType>(2),
|
|
static_cast<RealType>(1),
|
|
static_cast<RealType>(0.014388),
|
|
static_cast<RealType>(1-0.014388),
|
|
tolerance * 10); // one less decimal place in the test value
|
|
check_gamma(
|
|
static_cast<RealType>(3),
|
|
static_cast<RealType>(2),
|
|
static_cast<RealType>(5),
|
|
static_cast<RealType>(0.456187),
|
|
static_cast<RealType>(1-0.456187),
|
|
tolerance);
|
|
|
|
|
|
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a persentage
|
|
gamma_distribution<RealType> dist(8, 3);
|
|
RealType x = static_cast<RealType>(0.125);
|
|
using namespace std; // ADL of std names.
|
|
// mean:
|
|
BOOST_CHECK_CLOSE(
|
|
mean(dist)
|
|
, static_cast<RealType>(8*3), tol2);
|
|
// variance:
|
|
BOOST_CHECK_CLOSE(
|
|
variance(dist)
|
|
, static_cast<RealType>(8*3*3), tol2);
|
|
// std deviation:
|
|
BOOST_CHECK_CLOSE(
|
|
standard_deviation(dist)
|
|
, sqrt(static_cast<RealType>(8*3*3)), tol2);
|
|
// hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
hazard(dist, x)
|
|
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
|
|
// cumulative hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
chf(dist, x)
|
|
, -log(cdf(complement(dist, x))), tol2);
|
|
// coefficient_of_variation:
|
|
BOOST_CHECK_CLOSE(
|
|
coefficient_of_variation(dist)
|
|
, standard_deviation(dist) / mean(dist), tol2);
|
|
// mode:
|
|
BOOST_CHECK_CLOSE(
|
|
mode(dist)
|
|
, static_cast<RealType>(7 * 3), tol2);
|
|
// skewness:
|
|
BOOST_CHECK_CLOSE(
|
|
skewness(dist)
|
|
, 2 / sqrt(static_cast<RealType>(8)), tol2);
|
|
// kertosis:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis(dist)
|
|
, 3 + 6 / static_cast<RealType>(8), tol2);
|
|
// kertosis excess:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis_excess(dist)
|
|
, 6 / static_cast<RealType>(8), tol2);
|
|
|
|
BOOST_CHECK_CLOSE(
|
|
median(dist), static_cast<RealType>(23.007748327502412), // double precision test value
|
|
(std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as persent
|
|
// Rely on default definition in derived accessors.
|
|
|
|
// error tests
|
|
check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1);
|
|
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error);
|
|
|
|
} // template <class RealType>void test_spots(RealType)
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
// Basic sanity-check spot values.
|
|
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
|
test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
|
|
test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_spots(0.0L); // Test long double.
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
|
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
|
|
#endif
|
|
#else
|
|
std::cout << "<note>The long double tests have been disabled on this platform "
|
|
"either because the long double overloads of the usual math functions are "
|
|
"not available at all, or because they are too inaccurate for these tests "
|
|
"to pass.</note>" << std::endl;
|
|
#endif
|
|
|
|
|
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
|
|
|
|
|
/*
|
|
|
|
Output:
|
|
|
|
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe"
|
|
Running 1 test case...
|
|
Tolerance for type float is 0.000238419 %
|
|
Tolerance for type float is 0.001 %
|
|
Tolerance for type double is 5e-012 %
|
|
Tolerance for type double is 0.001 %
|
|
Tolerance for type long double is 5e-012 %
|
|
Tolerance for type long double is 0.001 %
|
|
Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
|
|
Tolerance for type class boost::math::concepts::real_concept is 0.001 %
|
|
*** No errors detected
|
|
|
|
*/
|
|
|
|
|